Abstract
Vehicle routing problem with time window (VRPTW) has been investigated by many researchers, in which the vehicle number is fixed in advance. In fact, the vehicle number can't be determined beforehand for practical problems. Because the fixed cost of a vehicle is much more than the running cost, and it is effective to cut down the total cost to seek the minimum number of vehicles in VRPTW. So, both the number and the routes of vehicles should be objectives of the VRPTW, which are described here. This paper presents a mathematical model of vehicle routing problem with time window with uncertain vehicle number. An improved chromosome representation that expresses the various vehicle numbers is proposed on the basis of customers. It is proved by an experiment that the genetic algorithm can search for the optimal solution for both route length and vehicle number.
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